Furnish means to supply a house with furniture. Refurnish means to replace existing furniture with new furniture. Decorate can mean many things: basically any "decoration." But this can vary from the wall decorations (paint, wallpaper, etc.) to the curtains to the carpet -- and also to the furniture and appliances. So decorate can have a broader meaning. The noun furnishings can refer to any of the previous except the actual walls. Redecorate, of course, means to change or replace existing decorations with new ones. But it does not have to mean every "decoration" or all the furnishings. Remodel can mean many things. But it usually refers to making a major change to all or part of the house. For example, to change one type of room to another, or make similar changes to part or all of the house. Refurbish usually refers to making a major improvement to a particular room or rooms. This usually includes upgrading existing structural, electrical, or plumbing elements. Since this is such a major change, you can say renovate also, since renovate means to make new again. But if you are renovating a whole house, that usually means no one is living there, OR the occupants (people living there) must move out while the renovations are being done. So renovate can mean either to make major changes to one room or the whole house. It does not have to apply to an old rundown house, but it can. In this situation, it means making an uninhabitable house habitable again.

I think you can also say furnish.

thank you! and is it correct to use the word renovate in the following situation: the house is on sale, then someone buys it, and the new owner doesn't like the decoration of the previous owner, so he decides to do everything again

'Decorate'. Renovate is only for older or broken properties.